How many guys in the NBA are above average players?

[payitforward]

It's the dog days of August. Moves have been made, but nothing's happening yet. Time to get all deep and thoughtful says I.

So, I ask you to please answer this question: how many guys who play in the league do you think are above average? Roughly speaking -- what percentage?

[dangermouse]

I think it depends on how you define average

[montestewart]

Some version of WS/48 or similar in some ratio with total win shares, then list players in order, then find the average from that list? If averaged, would that number be pulled down by 10 day call ups and such? Maybe consider a roster spot a player: one waived player, another signed to consecutive 10-days, and another signed to consecutive 10 days and then signed for the remainder of the season, all filling the same roster spot, averaged to produce the equivalent of one player on the list. Sounds like a lot of work, already giving me a headache.

How many Wizards are above average?

[nate33]

I figure about 49.9% of them are above average. Although, I guess that's not technically true. 49.9% of the minutes played are, by definition, above average; but presumably, the bulk of those above-average minutes are actually being played by a smaller subset of players since good players play more minutes.

There were 594822 total minutes played last year. That's 48 minutes per game, times 5 players, times 30 teams, plus a few extra overtime minutes. You could probably list all the players in the league and rank them by minutes played, and then just start from the top adding the minutes played. Once you've totaled 297411 minutes played (Half of 594822), stop counting players. The total number of players needed to reach 297411 is probably a good estimate of the total number of above average players.

[verbal8]

Some version of WS/48 or similar in some ratio with total win shares, then list players in order, then find the average from that list? If averaged, would that number be pulled down by 10 day call ups and such? Maybe consider a roster spot a player: one waived player, another signed to consecutive 10-days, and another signed to consecutive 10 days and then signed for the remainder of the season, all filling the same roster spot, averaged to produce the equivalent of one player on the list. Sounds like a lot of work, already giving me a headache.

How many Wizards are above average?

A real broad search of last season(realizing the limitations of both WS/48 and PER):
I limited the search to 500 minutes or greater which is 300 players in the league.

PER > 15.0 - 144
WS/48 > 0.10 - 159

114 of the players on both list overlapped

BTW salary - 130(MLE+) - no minute restriction

Wizards
6 - WS/48
3 - PER > 15

5 - salary > MLE

Your theoretical average team would have 5 above average starters, 5 below average subs and 2 to 5 players who play insignificant minutes.

With WS the top play-off teams seemed to have very high numbers of above average WS/48. PER seemed to be more evenly spread between teams.

[nate33]

I figure about 49.9% of them are above average. Although, I guess that's not technically true. 49.9% of the minutes played are, by definition, above average; but presumably, the bulk of those above-average minutes are actually being played by a smaller subset of players since good players play more minutes.

There were 594822 total minutes played last year. That's 48 minutes per game, times 5 players, times 30 teams, plus a few extra overtime minutes. You could probably list all the players in the league and rank them by minutes played, and then just start from the top adding the minutes played. Once you've totaled 297411 minutes played (Half of 594822), stop counting players. The total number of players needed to reach 297411 is probably a good estimate of the total number of above average players.

Here, I just did it for you. There are 122 above-average players in the league, give or take. Going by PER, the 122nd best player was Danny Green. Going by WS/48, it was DeMarcus Cousins.

[Dat2U]

Ok, here's what I come up with:

Franchise changing superstars

1. F LeBron James
2. F Kevin Durant
3. G Chris Paul

Legitimate 1st options / all-star caliber talent

4. G Derrick Rose
5. G James Harden
6. G Tony Parker
7. F Blake Griffin
8. G Russell Westbrook
9. G Dwyane Wade
10. C Tim Duncan
11. C Brook Lopez
12. F Carmelo Anthony
13. G Deron Williams
14. G Stephen Curry
15. G Kobe Bryant

Elite level role players

16. C Tyson Chandler
17. C Marc Gasol
18. C Tiago Splitter
19. F Serge Ibaka
20. F David West
21. G George Hill
22. C Chris Bosh
23. C Anderson Varejao
24. G Mike Conley
25. C Andre Drummond
26. F Kawhi Leonard

Very good starters

27. F Amar'e Stoudemire
28. F Kenneth Faried
29. G Jose Calderon
30. C Nikola Pekovic
31. F Anthony Davis
32. F Ersan Ilyasova
33. G Kevin Martin
34. F Paul Millsap
35. C Al Horford
36. F Danilo Gallinari
35. F Amir Johnson
36. F David Lee
37. C Larry Sanders
38. C DeAndre Jordan
39. F Paul George
40. C Joakim Noah
41. F Dirk Nowitzki
42. F Zach Randolph
43. C Al Jefferson
44. G Ty Lawson
45. F Thaddeus Young
46. F Paul Pierce
47. C Dwight Howard
48. G John Wall
49. C Roy Hibbert
50. G Kyle Lowry

Very good role players

51. C Brandan Wright
52. C Kosta Koufos
53. C Javale McGee
54. F Ed Davis
55. F Carl Landry
56. G Jimmy Butler
57. C Nick Collison
58. G Manu Ginobili
59. F Tyler Hansbrough
60. C Andray Blatche
61. G Patrick Beverley
62. F Matt Barnes
63. G Thabo Sefolosha
64. F Jared Sullinger
65. F J.J. Hickson
66. F Andrei Kirilenko
67. F Martell Webster
68. F Vince Carter
69. F Wilson Chandler
70. F Kyle Korver
71. G Nate Robinson
72. C Kevin Garnett
73. F Dorell Wright
74. G Danny Green
75. F Shawn Marion
76. G Ray Allen
77. G Steve Nash
78. C Robin Lopez

Quality starters

79. C Jonas Valanciunas
80. F Ryan Anderson
81. G Kyrie Irving
82. F LaMarcus Aldridge
83. F Gordon Hayward
84. F Chandler Parsons
85. G Mario Chalmers
86. G J.R. Smith
87. F Derrick Favord
88. G Jamal Crawford
89. F Nene
90. G Tony Allen
91. G Eric Bledsoe
92. G Jarrett Jack
93. G Lance Stephenson
94. G Isaiah Thomas
95. G Jeff Teague
96. C Omer Asik
97. F Carlos Boozer
98. G Rajon Rondo
99. F Pau Gasol
100. G Goran Dragic
101. C Andrew Bogut
102. C Nikola Vucevic
103. F Loul Deng
104. G Tyreke Evans
105. C Greg Monroe
106. F Brandon Bass
107. F Nicolas Batum
108. F Jeff Green
109. F Danny Granger

Quality role players

110. C Chris Andersen
111. C Jordan Hill
112. G Chauncey Billups
113. C Samuel Dalembert
114. F Mike Miller
115. F DeMarre Carroll
116. F Matt Bonner
117. F Jeff Pendergraph
118. C Kenyon Martin
119. F DeJuan Blair
120. F Trevor Booker
121. F Antawn Jamison
122. F Quincy Pondexter
123. F Boris Diaw
124. G Pablo Prigioni
125. G Reggie Jackson
126. G Andre Miller
127. G C.J. Watson
128. F Shane Battier
129. F Chris Copeland
130. F Steve Novak
131. C Zaza Pachulia
132. G Darren Collison
133. G Devin Harris
134. G D.J. Augustin
135. F Patrick Patterson
136. F Mike Dunleavy
137. F Taj Gibson
138. F John Henson
139. F Kris Humphries
140. G Jerryd Bayless
141. F Udonis Haslem
142. C Elton Brand
143. F Jared Dudley
144. F Reggie Evans
145. C Marreese Speights
146. G Louis Williams

[dobrojim]

IDK, about half.

[nate33]

C'mon Dat2U. You've become the ultimate anti-homer. I hope the absence of Okafor on the list was an oversight and that you don't actually consider the likes of Reggie Evans, Antawn Jamison, Matt Bonner, Demarre Carroll and Chris Copeland to be better than him. How can Amare Stoudemire be ranked 27th and Nene 89th? Wall is 48th while Jose Calderon is 29th?

You've got a bunch of other highly questionable rankings. Drummond is 25th while Aldridge is 82nd? Kawhi Leonard is 26th while Paul George is 39th? Tyler Hansbrough is the 59th best player in the league and would therefore be the 3rd best player on nearly any team? Patrick Beverley is 61st with Asik 96th?

[Zonkerbl]

IDK, about half.

That's what I was going to say, but it's not true, funny as that would be to say.

The talent level in the NBA is not bell curved, with most players being average and a small number of really bad players and a small number of really good ones. If that were the case yes, half of the players would have above average talent. But we don't select NBA players randomly from the population at large. We select players from the top end of the talent distribution.

Since we're selecting a pretty decent sample of players (about 300), the probability distribution of talent in the NBA is approximately exponential:
http://en.wikipedia.org/wiki/Exponential_distribution

where the highest concentration of players is actually at the lowest level of talent that can get you on a roster (the CBA structure may skew this a little, but basically that's what's going on). Because of this "skewness" in the distribution of talent, the "average" talent level will be above the median. So actually less than half of the players would have "above average" talent. So if the average talent level = 1, the median player will have a talent level of about 0.7. Or to put it another way, the median player's talent level is actually one standard deviation below the mean!

The cumulative distribution function for an exponential distribution with a mean of 1 is F(x)=1-exp(-x), so the probability of having talent greater than average is exp(-1)=36.8%. So a little more than a third of the players in the NBA have "above average" talent.

So. If there are 30 teams with 12 players each (360 players total), about 132 are above average. So your method of weighting players by minutes played just about nailed it.

I really need to start teaching statistics. These real life examples are worth their weight in gold.

[payitforward]

With WS the top play-off teams seemed to have very high numbers of above average WS/48. PER seemed to be more evenly spread between teams.

That should tell you which measure better reflects the things players do to win or lose games, don't you think?

[payitforward]

The talent level in the NBA is not bell curved, with most players being average and a small number of really bad players and a small number of really good ones. If that were the case yes, half of the players would have above average talent. But we don't select NBA players randomly from the population at large. We select players from the top end of the talent distribution.

Since we're selecting a pretty decent sample of players (about 300), the probability distribution of talent in the NBA is approximately exponential:
http://en.wikipedia.org/wiki/Exponential_distribution

where the highest concentration of players is actually at the lowest level of talent that can get you on a roster (the CBA structure may skew this a little, but basically that's what's going on). Because of this "skewness" in the distribution of talent, the "average" talent level will be above the median. So actually less than half of the players would have "above average" talent. So if the average talent level = 1, the median player will have a talent level of about 0.7. Or to put it another way, the median player's talent level is actually one standard deviation below the mean!

The cumulative distribution function for an exponential distribution with a mean of 1 is F(x)=1-exp(-x), so the probability of having talent greater than average is exp(-1)=36.8%. So a little more than a third of the players in the NBA have "above average" talent.

So. If there are 30 teams with 12 players each (360 players total), about 132 are above average. So your method of weighting players by minutes played just about nailed it.

I really need to start teaching statistics. These real life examples are worth their weight in gold.

Good work!

Now, the distribution of minutes compensates for the exponential distribution of productivity (productivity not "talent"), and this is true by definition. Thus if you correct for number of minutes played, you do get a bell-shaped curve.

[Dat2U]

C'mon Dat2U. You've become the ultimate anti-homer. I hope the absence of Okafor on the list was an oversight and that you don't actually consider the likes of Reggie Evans, Antawn Jamison, Matt Bonner, Demarre Carroll and Chris Copeland to be better than him. How can Amare Stoudemire be ranked 27th and Nene 89th? Wall is 48th while Jose Calderon is 29th?

You've got a bunch of other highly questionable rankings. Drummond is 25th while Aldridge is 82nd? Kawhi Leonard is 26th while Paul George is 39th? Tyler Hansbrough is the 59th best player in the league and would therefore be the 3rd best player on nearly any team? Patrick Beverley is 61st with Asik 96th?

My bad I should have explained it, its not in order from top to bottom. I tried to categorize things to make it a bit easier to digest. IMO the order depends on how your value role players in smaller roles vs. high usage players who may not have the efficiency. After the top 15 or so, trying to rank them gets kinda sketchy. Too many different variables to look at IMO to get a clear answer. So that's why I've tried to separate role players from starters.

I left Okafor & Ariza off the list by accident just b/c I'm an airhead. Okafor is a quality starter who should have been 105/106. Ariza is a quality reserve.

By my count the Wizards have 6 average to above average players: Wall, Nene, Okafor, Webster, Ariza & Booker though Beal may certainly get there this year.

[payitforward]

C'mon Dat2U. You've become the ultimate anti-homer. I hope the absence of Okafor on the list was an oversight and that you don't actually consider the likes of Reggie Evans, Antawn Jamison, Matt Bonner, Demarre Carroll and Chris Copeland to be better than him. How can Amare Stoudemire be ranked 27th and Nene 89th? Wall is 48th while Jose Calderon is 29th?

You've got a bunch of other highly questionable rankings. Drummond is 25th while Aldridge is 82nd? Kawhi Leonard is 26th while Paul George is 39th? Tyler Hansbrough is the 59th best player in the league and would therefore be the 3rd best player on nearly any team? Patrick Beverley is 61st with Asik 96th?

Emeka had the 17th highest ws48 among all Centers who played more than 5 minutes for the whole year, so yes he belongs on that list. I assume that's an oversight.

Calderon is ranked higher than Wall because on the year he played better than Wall -- much better.

Kawhi Leonard is ranked higher than Paul George because his WS48 was much higher. PERs were very close, because Paul George shoots more. If you shoot 30% or higher, your PER goes up every time you take a shot. I like Paul George, he's a very very good player. Leonard, however, is clearly better -- fouls less, turns it over much less, gets more offensive rebounds, shoots a higher FT% and has a much higher TS%. He had the 5th highest ws48 of all 3s in the league.

Nene and Stoudamire had almost identical ws48 -- Stoudamire's PER was much higher, however, again because PER overvalues scoring vs. other stuff.

As to Drummond -- he only played @1000 minutes. During those minutes he was the most productive Center in the league -- only Tim Duncan was close. Every 40 minutes, Drummond got 15 points on 61% shooting, and he had 15 boards as well, and basically never turned it over either. Guy's a monster. Wait til he has a full season.

Asik's raiting makes no sense, as he was one of the top Centers in the league. But Beverly played great, so his rating is no surprise.

[dobrojim]

I guess I made the mistake of assuming that the question really was
how many guys are above average /NBA/ players which would make
the answer of about 50% probably pretty close on a first approximation.

If the question is just above average players, then the answer is
probably something approaching 100%.

[Zonkerbl]

I guess I made the mistake of assuming that the question really was
how many guys are above average /NBA/ players which would make
the answer of about 50% probably pretty close on a first approximation.

If the question is just above average players, then the answer is
probably something approaching 100%.

Actually a little over a third of NBA players are "above average."

Miiiiiind fliiiiiiip!!!!

[Zonkerbl]

So. If there are 30 teams with 12 players each (360 players total), about 132 are above average. So your method of weighting players by minutes played just about nailed it.

I really need to start teaching statistics. These real life examples are worth their weight in gold.

Good work!

Now, the distribution of minutes compensates for the exponential distribution of productivity (productivity not "talent"), and this is true by definition. Thus if you correct for number of minutes played, you do get a bell-shaped curve.

That's what I said!

[Dat2U]

Emeka had the 17th highest ws48 among all Centers who played more than 5 minutes for the whole year, so yes he belongs on that list. I assume that's an oversight.

Oversight, yes. 17th highest? No.

Ordered by WS/48. Any C that played more than 1,000 minutes last season (injury exceptions: Varejao & Bogut). I think people forget how deep the C position is in the league today. There may not be a ton of star power, but there's a lot of quality bigs out there. Okafor is closer to the bottom than to the top of the list.
1. T. Chandler
2. M. Gasol
3. T. Splitter
4. T. Duncan
5. B. Lopez
6. C. Bosh
7. A. Varejao
8. A. Drummond
9. G. Smith
10. B. Wright
11. K. Koufos
13. J. McGee
14. N. Pekovic
15. N. Collison
16. A. Blatche
17. A. Horford
18. L. Sanders
19. D. Jordan
20. J. Noah
21. A. Jefferson
22. J. Hickson
23. D. Howard
24. R. Hibbert
25. J. Valanciunas
26. R. Lopez
27. Z. Pachulia
29. A. Bogut
30. N. Vucevic
31. G. Monroe
32. E. Okafor
33. M. Leonard
34. E. Kanter
35. S. Hawes
36. D. Cousins
37. J. O'Neal
38. M. Gortat
39. I. Mahinmi
40. L. Allen
41. G. Steimsma
42. F. Ezeli
43. K. Perkins
44. C. Hayes
45. C. Kaman
46. T. Zeller
47. B. Biyombo
48. A. Bargnani
49. B. Haywood
50. K. Seraphin

[montestewart]

I guess I made the mistake of assuming that the question really was
how many guys are above average /NBA/ players which would make
the answer of about 50% probably pretty close on a first approximation.

If the question is just above average players, then the answer is
probably something approaching 100%.

Actually a little over a third of NBA players are "above average."

Miiiiiind fliiiiiiip!!!!

Does that make below average more tolerable or less tolerable?

[Zonkerbl]

I guess I made the mistake of assuming that the question really was
how many guys are above average /NBA/ players which would make
the answer of about 50% probably pretty close on a first approximation.

If the question is just above average players, then the answer is
probably something approaching 100%.

Actually a little over a third of NBA players are "above average."

Miiiiiind fliiiiiiip!!!!

Does that make below average more tolerable or less tolerable?

Well... If almost two thirds of the league is below average...